The 24-year-old, part of Liverpool's FA Youth Cup-winning side in 2009, featured over 100 times for Nottingham Forest prior to the expiry of his contract at the City Ground.
Manager Derek McInnes told the Robins' official website: "I'm delighted to have completed this capture.
"He is a player with bags of potential, who knows the Championship with years of experience in the division and arrives at a decent age.
"He has real pace, can play in two or three different roles and is a good addition to strengthen our team and squad.
"He has his best years ahead of him and we've beaten a number of other clubs to his signature."
Anderson will link up with the squad for their tour of Scotland and could be handed his debut when the Robins meet McInnes' former employers St Johnstone on Friday.